作业帮根号下[x^2+(y+4)^2] + 根号下[x^2+(y-4)^2] = 12
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/05 20:55:22
根号下[x^2+(y+4)^2] + 根号下[x^2+(y-4)^2] = 12
根号下[x^2+(y+4)^2] + 根号下[x^2+(y-4)^2] = 12
√[x^2+(y+4)^2] + √[x^2+(y-4)^2] = 12
[x^2+(y+4)^2] + 2√[x^2+(y+4)^2][x^2+(y-4)^2] +[x^2+(y-4)^2] = 144
x^2+y^2+8y+16 + 2√[x^2+(y+4)^2][x^2+(y-4)^2] +x^2+y^2-8y+16 = 144
√[x^2+(y+4)^2][x^2+(y-4)^2] =56-x^2-y^2
[x^2+(y+4)^2][x^2+(y-4)^2] =56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
[x^2+(y+4)^2][x^2+(y-4)^2] =56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
x^4+((y+4)^2+(y-4)^2)x^2+(y^2-16)^2=56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
x^4+2x^2y^2+32x^2+y^4-32y^2+16^2=56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
2880-144x^2-80y^2=0
180-9x^2-5y^2=0
√[x^2+(y+4)^2] + √[x^2+(y-4)^2] = 12
[x^2+(y+4)^2] + 2√[x^2+(y+4)^2][x^2+(y-4)^2] +[x^2+(y-4)^2] = 144
x^2+y^2+8y+16 + 2√[x^2+(y+4)^2][x^2+(y-4)^2] +x^2+y^2-8y+16 = 144
√[x^2+(y+4)^2][x^2+(y-4)^2] =56-x^2-y^2
[x^2+(y+4)^2][x^2+(y-4)^2] =56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
[x^2+(y+4)^2][x^2+(y-4)^2] =56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
x^4+((y+4)^2+(y-4)^2)x^2+(y^2-16)^2=56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
x^4+2x^2y^2+32x^2+y^4-32y^2+16^2=56^2+x^4+y^4-112x^2-112y^2+2x^2y^2
2880-144x^2-80y^2=0
180-9x^2-5y^2=0
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